œ-conjugation and nonconvex optimization. a survey (part i)

Abstract

In some papers, the authors developed the theory of œconjugate functions. By this notion a broad class of nonconvex optimization problems had been investigated successfully. The present paper, which is the first part of a comprehensive overview, generalizes former investigations to the infinite dimensional case whereby linear (topo-logical) spaces are used. We give properties of œ-conjugate functions, among others the inequality corresponding to the classical Fenchel inequality, a characterization of supporting hyperplanes and the connection with biconjugate functions. Furthermore, some duality theorems for nonconvex optimization problems are proved and illustrated by corresponding examples.